Following the Z-estimation principle [1]}, [2]}, one could define the final estimator of \(\theta \)  as the solution of the pseudo-score function \(\hat{h}(\theta , \hat{})\) . However, in many examples, the pseudo-score function \(\hat{h}(\theta , \hat{})\)  may have multiple solutions and it becomes unclear which root serves as a consistent estimator; see [3]} for further discussion in the general estimating function context. To bypass this issue, we consider the following simple one-step estimation approach. Given the initial estimator \(\hat{\theta }\)  from the partition of \(\hat{}\) , we perform a Newton-Raphson update based on the pseudo-score function \(\hat{h}(\theta , \hat{})\) ,
to obtain \(\tilde{\theta }\) , which is classically referred to as a one-step estimator by [4]}. Specifically, we construct
\(\tilde{\theta }=\hat{\theta }-\hat{}_{1|2}^{-1}\hat{h}(\hat{\theta },\hat{}),\) 
